Answer :
Let's solve each part using a mental math trick that involves rounding to a nearby “nice” number, and then adjusting the result.
–––––––
a. Calculation:
We want to calculate
[tex]$$
99 + 54.
$$[/tex]
Notice that [tex]$99$[/tex] is just [tex]$1$[/tex] less than [tex]$100$[/tex]. So we can think:
1. Replace [tex]$99$[/tex] by [tex]$100$[/tex]. Then,
[tex]$$
100 + 54 = 154.
$$[/tex]
2. Since we added [tex]$1$[/tex] extra when using [tex]$100$[/tex], subtract [tex]$1$[/tex] from [tex]$154$[/tex]:
[tex]$$
154 - 1 = 153.
$$[/tex]
Thus,
[tex]$$
99 + 54 = 153.
$$[/tex]
–––––––
b. Calculation:
We want to calculate
[tex]$$
244 - 99.
$$[/tex]
Here, it is often easier to subtract [tex]$100$[/tex] instead of [tex]$99$[/tex]. So, we can do:
1. Subtract [tex]$100$[/tex] from [tex]$244$[/tex]:
[tex]$$
244 - 100 = 144.
$$[/tex]
2. Since we subtracted [tex]$1$[/tex] too much (we subtracted [tex]$100$[/tex] instead of [tex]$99$[/tex]), we add back [tex]$1$[/tex]:
[tex]$$
144 + 1 = 145.
$$[/tex]
Thus,
[tex]$$
244 - 99 = 145.
$$[/tex]
–––––––
c. Calculation (i):
We want to calculate
[tex]$$
99 \times 6.
$$[/tex]
Again, think of [tex]$99$[/tex] as [tex]$100 - 1$[/tex].
1. Multiply [tex]$100$[/tex] by [tex]$6$[/tex]:
[tex]$$
100 \times 6 = 600.
$$[/tex]
2. Since [tex]$99$[/tex] is [tex]$1$[/tex] less than [tex]$100$[/tex], we subtract [tex]$6$[/tex] (that is, [tex]$1 \times 6$[/tex]) from [tex]$600$[/tex]:
[tex]$$
600 - 6 = 594.
$$[/tex]
Thus,
[tex]$$
99 \times 6 = 594.
$$[/tex]
–––––––
d. Calculation (ii):
Next, we calculate
[tex]$$
99 \times 15.
$$[/tex]
Use the same idea:
1. Multiply [tex]$100$[/tex] by [tex]$15$[/tex]:
[tex]$$
100 \times 15 = 1500.
$$[/tex]
2. Subtract the extra [tex]$15$[/tex] (since we used [tex]$100$[/tex] instead of [tex]$99$[/tex], we subtract [tex]$1 \times 15$[/tex]):
[tex]$$
1500 - 15 = 1485.
$$[/tex]
Thus,
[tex]$$
99 \times 15 = 1485.
$$[/tex]
–––––––
Final Answers:
[tex]\[
\begin{aligned}
a.\quad 99 + 54 &= 153,\\[1mm]
b.\quad 244 - 99 &= 145,\\[1mm]
c.\quad 99 \times 6 &= 594,\\[1mm]
\quad 99 \times 15 &= 1485.
\end{aligned}
\][/tex]
These mental math strategies help simplify calculations by replacing awkward numbers with round numbers and then making a simple adjustment.
–––––––
a. Calculation:
We want to calculate
[tex]$$
99 + 54.
$$[/tex]
Notice that [tex]$99$[/tex] is just [tex]$1$[/tex] less than [tex]$100$[/tex]. So we can think:
1. Replace [tex]$99$[/tex] by [tex]$100$[/tex]. Then,
[tex]$$
100 + 54 = 154.
$$[/tex]
2. Since we added [tex]$1$[/tex] extra when using [tex]$100$[/tex], subtract [tex]$1$[/tex] from [tex]$154$[/tex]:
[tex]$$
154 - 1 = 153.
$$[/tex]
Thus,
[tex]$$
99 + 54 = 153.
$$[/tex]
–––––––
b. Calculation:
We want to calculate
[tex]$$
244 - 99.
$$[/tex]
Here, it is often easier to subtract [tex]$100$[/tex] instead of [tex]$99$[/tex]. So, we can do:
1. Subtract [tex]$100$[/tex] from [tex]$244$[/tex]:
[tex]$$
244 - 100 = 144.
$$[/tex]
2. Since we subtracted [tex]$1$[/tex] too much (we subtracted [tex]$100$[/tex] instead of [tex]$99$[/tex]), we add back [tex]$1$[/tex]:
[tex]$$
144 + 1 = 145.
$$[/tex]
Thus,
[tex]$$
244 - 99 = 145.
$$[/tex]
–––––––
c. Calculation (i):
We want to calculate
[tex]$$
99 \times 6.
$$[/tex]
Again, think of [tex]$99$[/tex] as [tex]$100 - 1$[/tex].
1. Multiply [tex]$100$[/tex] by [tex]$6$[/tex]:
[tex]$$
100 \times 6 = 600.
$$[/tex]
2. Since [tex]$99$[/tex] is [tex]$1$[/tex] less than [tex]$100$[/tex], we subtract [tex]$6$[/tex] (that is, [tex]$1 \times 6$[/tex]) from [tex]$600$[/tex]:
[tex]$$
600 - 6 = 594.
$$[/tex]
Thus,
[tex]$$
99 \times 6 = 594.
$$[/tex]
–––––––
d. Calculation (ii):
Next, we calculate
[tex]$$
99 \times 15.
$$[/tex]
Use the same idea:
1. Multiply [tex]$100$[/tex] by [tex]$15$[/tex]:
[tex]$$
100 \times 15 = 1500.
$$[/tex]
2. Subtract the extra [tex]$15$[/tex] (since we used [tex]$100$[/tex] instead of [tex]$99$[/tex], we subtract [tex]$1 \times 15$[/tex]):
[tex]$$
1500 - 15 = 1485.
$$[/tex]
Thus,
[tex]$$
99 \times 15 = 1485.
$$[/tex]
–––––––
Final Answers:
[tex]\[
\begin{aligned}
a.\quad 99 + 54 &= 153,\\[1mm]
b.\quad 244 - 99 &= 145,\\[1mm]
c.\quad 99 \times 6 &= 594,\\[1mm]
\quad 99 \times 15 &= 1485.
\end{aligned}
\][/tex]
These mental math strategies help simplify calculations by replacing awkward numbers with round numbers and then making a simple adjustment.
